Show the graph of the 3/3

Mathematics

ScanSolve AI Answer

Answer

To show the graph, you would plot the Cost and Revenue functions on a coordinate plane.

Graph of R(x) = 0.46x

Use the left and right arrow keys to trace the curve, up and down to jump between key points, and plus and minus to zoom.

Key points of R(x) = 0.46x
Pointxy
x-intercept00

Step-by-step solution

4 steps
  1. Set up the axes.

    • The horizontal axis (x-axis) represents the Number of Bottles Produced and Sold.
    • The vertical axis (y-axis) represents Total Cost/Revenue (₦).
  2. Plot the Cost Function C(x)=10,000+0.03xC(x) = 10,000 + 0.03x.

    • This is a straight line.
    • Y-intercept (Fixed Cost): When x=0x=0, C(0)=10,000C(0) = 10,000. Plot the point (0,10,000)(0, 10,000).
    • Cost at Maximum Annual Capacity: When x=600,000x=600,000, C(600,000)=10,000+0.03×600,000=28,000C(600,000) = 10,000 + 0.03 \times 600,000 = 28,000. Plot the point (600,000,28,000)(600,000, 28,000).
    • Draw a straight line connecting these two points.
  3. Plot the Revenue Function R(x)=0.46xR(x) = 0.46x.

    • This is also a straight line.
    • Origin: When x=0x=0, R(0)=0R(0) = 0. Plot the point (0,0)(0, 0).
    • Revenue at Maximum Annual Capacity: When x=600,000x=600,000, R(600,000)=0.46×600,000=276,000R(600,000) = 0.46 \times 600,000 = 276,000. Plot the point (600,000,276,000)(600,000, 276,000).
    • Draw a straight line connecting these two points.
  4. Identify the Break-Even Point.

    • The break-even point is where the Cost line and the Revenue line intersect.
    • From the previous calculation, the break-even point is approximately (23,256 bottles,₦10,697.76)(\text{23,256 bottles}, \text{₦10,697.76}). Mark this intersection point on your graph.

    Description of the Graph:
    You will see two straight lines originating from the y-axis.

    • The Cost line starts at ₦10,000 on the y-axis and slopes upwards.
    • The Revenue line starts at ₦0 (the origin) and slopes upwards more steeply than the cost line.
    • The point where these two lines cross is the break-even point. To the left of this point, the cost line is above the revenue line, indicating a loss. To the right of this point, the revenue line is above the cost line, indicating a profit.
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